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Mathematical Charts and Tables

Special Purpose Tables

Special Purpose Tables

From at least the 1930s through the 1960s, American manufacturers distributed a variety of tables that customers might use. This was sometimes in the form of a pamphlet, such as the set of miscellaneous hydraulic tables for designers prepared by the Southwark Foundry and Machine Company Division of Baldwin-Southwark Corporation in 1931. Other special purpose tables, distributed on slide charts of various sorts, described properties of such materials as leaded bronze, nickel alloys, specialty steels, wire cloth, glass, and salt/water mixtures. Others gave properties of compressors, elements of screw threads, and data on the dietary advantages of various forms of meat, The Aetna insurance company prepared a table instructing drivers on the safe distances to be maintained between cars. As late as 1969, a manufacturer of paper goods distributed a slide chart for calculating the cost per ounce of groceries, and urged consumers to make careful comparisons of prices. Some tables were not associated with any specific product. Thus the “Menu Minder,” distributed in the mid-1970s, allowed one to quickly alter recipes to serve more or fewer people. It may have been distributed as a kitchen novelty by any number of firms.

Tables distributed by business machine manufacturers have been mentioned already. In addition to covering the needs of commerce and special forms of manufacturing, some of these offered ways to estimate square roots and cube roots.

Specialized tables also were prepared for government use. Military contractors prepared tables to assist in aiming guns and filling out Air Force inventory forms. The Atomic Energy Commission prepared a table for use in uranium enrichment plants.

This slide chart, distributed by the Qunicy Compressor company of Quincy, Illinois, is designed to allow customers to select the appropriate model of Quincy air compressor to purchase, knowing the pressure at which the air is to be delivered and the number of cubic feet per minute of air delivery desired. On one side, pressures range from 30 to 100 pounds On the other, they range from 110 to 250 pounds. For each model, the chart indicates the horsepower, speed, and piston displacement.

The chart consists of a paper envelope held together with metal rivets and a paper slide that moves crosswise. A mark near the bottom reads: Copyright 1941 Perry Graf Corp. Maywood, Ill. Slide charts made by Perry Graf that are in the Museum collections include 1979.3074.03, 1983.3009.04, 1983.3009.05,1983.3009.06, 1987.0108.03, and 1988.0325.01, and 1988.3076.01.

Mathematical tables like this one were distributed by producers to persuade consumers of the value of their products. This instrument consists of a disc with a smaller disc that rotates above it. A metal clasp at the center holds the two pieces together. A slot in the upper disc reveals one column of the table printed on the disc below. This table gives the percentage of daily recommended dietary allowances supplied by a 3.5 oz serving of beef, lamb, pork, and veal. The percentages are given for children of ages 3-4 years, 4-6 years, 7-9 years, and 10-12 years; teenaged boys 13-15 and 16-19 years old; teenaged girls 13-15 and 16-19 years old; women of ages 25, 45, and 65; and men of ages 25, 45, and 65. The daily requirements of protein, calories, iron, thiamine, riboflavin, and niacin supplied by a serving of meat are indicated. The back lists the nutrition provided by strained meat fed to infants and gives references for the calculations. These references date from 1950 and 1958.

The instrument is marked on the front: The percentages of (/) daily recommended dietary (/) allowances supplied by one (/) 3 1/2 oz. serving of cooked MEAT for moderately active children and adults. It is marked on the front and the back: NATIONAL LIVE STOCK AND MEAT BOARD. It is marked on the back: A Product of Graphic Calculator Co., Chicago 5, Ill.

Graphic Calculator Company was a slide rule and slide chart manufacturing and design company founded in Chicago in 1940 by Capron R. Gulbransen, and apparently still in business at the time of Gulbransen’s death in 1969. By 1965, the firm had moved to Barrington, Illinois.

By the mid-20th century, industrial chemists had introduced a form of hydrometer for measuring brine strength from the density of a water/salt solution at a known temperature. This rotating table allows one to find the chemical properties of solutions of sodium chloride (common table salt) in water at a temperature of 60 degrees Fahrenheit in degrees of the “salometer scale.” By definition, the salometer degree indicates percentage of saturation of a salt solution. For example, a reading of 70 indicates 70% saturation. Hence the scale runs from 0 to 100.

The slide chart consists of two paper discs of the same size, with a third slightly larger disc between them. The middle disc is elongated at one end and has a hole so that it may be suspended. A metal rivet holds the discs together at the center. Cutouts in the two smaller discs allow one to read tables printed on the central disc. The front of the instrument has tables for 0 to 50, and the reverse for 51 to 100. For each salometer degree, the table lists such chemical properties of the solution as its specific gravity, the percentage by weight of sodium chloride, the weight in pounds of one gallon of brine, the number of pounds per gallon of brine of both sodium chloride and water, the weight of one cubic foot of brine, the number of pounds per cubic foot of both sodium chloride and water, the number of gallons of water per gallon of brine, the number of pounds of salt per gallon of water, and the freezing point in degrees Fahrenheit. Another table indicates how one should adjust readings in degrees salometer when measurements are taken at temperatures other than 60 degrees Fahrenheit.

A mark on the top disc reads: BRINEMASTER (/) dial-a-brine. A second mark there reads: Diamond Crystal Salt Company (/) ST. CLAIR, MICHIGAN. A mark on the bottom disc reads: Slide-Chart Copr. [sic] 1962, PERRYGRAF Corp., Maywood, Ill.

The salinity of brines was expressed in salometer degrees from at least the 19th century.

References:

L. C. Beck, “Report on the Mineralogical and Chemical Department of the Survey,” In Assembly: State of New York, Issue 150, 1841, p. 18.

E. Meriam, “American and Foreign Salt,” Sixth Annual Report of the American Institute of the City of New York, 1848, p. 207.

This chart has a black image marked on a rigid white plastic sheet. Five equally spaced concentric circles are divided into eight equal sections by lines through the center of the circle. The outermost circle is divided into 64 equal segments, which are numbered counterclockwise from 0 to 32 on the left half of the circle. On the right half, segments are numbered from 0 at the bottom counterclockwise to 30 at the top, and also from (34) to (64).

A mark at the bottom left reads: CARD, TANK RANGE (/) 8724207. A mark on the left top reads: HUNDREDS OF MILS. There are 6400 mils in a circle of 360 degrees angular measure.

The object comes from the Felsenthal Collection of computing devices. According to the accession file it was made by Felsenthal for the U.S. Army in 1955, and had Felsenthal designation FA0-51. It may have been used by the tank gunner to lay his gun on target, before the availability of electronic or laser sighting.

This device assists in calculations of changes in the range of a gun because of meteorological conditions, particularly wind speed and temperature. A rotating disc and pointer attached to the plastic base have the scales required to correct for wind speed. A scale toward the bottom of the base gives the temperature correction. Both of these corrections are in percentages of the range. Summing them gives the total meteorological correction as a percentage of the range. One then can use a range correction chart to find the actual range correction.

This white plastic chart was designed for the U.S. Army Signal Corps. It is a nomogram for finding the range correction in yards of a weapon, by lining up the meteorological correction as a percentage of the range and the range.

On the left is a scale marked “Range Correction in Yds.” On the right is a scale marked “Percentage Meteorological Correction” and on the diagonal between the two is a scale marked “Range in Yds.” According to a label received with the object and stored in the accession file, the object was made in 1945.

The meteorological correction is found from the temperature and wind speed using a related chart called a “sound velocity corrector” (for an example, see 1977.1141.42) .

A mark on the object reads: Range Correction Chart PT-63/TSS-1.

For an explanation of the mathematical theory of this kind of nomogram, see Lipka. For a similar device used for another purpose, see 1985.0636.01.

This slide chart is designed to assist in coding United States Air Force forms for inventory control. The envelope is of clear plastic printed in blue, with a white plastic card that slides crosswise. The sliding card has columns for eight Air Force forms (forms number 158A&B, 158C&D, 813, 814, 815, 158-7, 366J&K, and 366L&M). The numbers in each column indicate the place on the form on which the data is to be entered. For example, in all eight forms spaces 1through15 are for the stock number and spaces 31through 34 are for the organization number. The first 56 spaces are described on the front of the sliding card. The remainder (up to 80) are on the back.

It is possible that the forms described are 80-column punch cards, such as those made by IBM for use with electronic data processing equipment.

A mark on the front of the envelope reads: Code Designator (/) Slide Chart. A mark on the back of the envelope reads: Felsenthal Instruments Co.1963 (/) Chicago 31, Illinois (/) MFR’s PT.NO. FAA-141-A.